Two L shaped arears that will not allow me to build on, walk in or jump across.

[vestal shuttle]

see photo, self explanatory.

[arctic quartz]

Are you trying to link two platforms that have power that inputs to a base building? Because if you are, the game won't let you do that. Each platform can only provide one input to base power.

The moment you unplug either cable, the game will let you build there.